Wikipedia:WikiProject Mathematics/PlanetMath Exchange/42-XX Fourier analysis

This page provides a list of all articles available at PlanetMath in the following topic:

42-XX Fourier analysis.

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A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

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42-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: discrete cosine transform, id=1469 -- WP: discrete cosine transform -- Status: A

CryptoDerk 21:27, Feb 2, 2005 (UTC)

42-01 Instructional exposition (textbooks, tutorial papers, etc.)

• PM: Laplace transform, id=4343 -- WP: Laplace transform -- Status: A

CryptoDerk 21:37, Feb 2, 2005 (UTC)

42A05 Trigonometric polynomials, inequalities, extremal problems

• PM: Chebyshev polynomial, id=2161 -- WP: Chebyshev polynomial -- Status: A

CryptoDerk 21:59, Feb 2, 2005 (UTC)

42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series

• PM: example of Fourier series, id=4718 -- WP: Fourier series -- Status: M

CryptoDerk 23:05, Feb 2, 2005 (UTC)

• PM: Riemann-Lebesgue lemma, id=3571 -- WP: Riemann-Lebesgue lemma -- Status: C

CryptoDerk 01:56, Feb 3, 2005 (UTC)

42A20 Convergence and absolute convergence of Fourier and trigonometric series

• PM: Dirichlet conditions, id=3891 -- WP: Dirichlet conditions -- Status: A

The PM article is actually fairly ambiguous. It states truths, but doesn't really give a hard definition for the conditions. CryptoDerk 02:31, Feb 3, 2005 (UTC)

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

• PM: Fourier transform, id=2823 -- WP: Fourier transform -- Status: A

Kind of spread out amongst various articles, including continuous Fourier transform and related articles linked to from the main Fourier transform article. CryptoDerk 02:51, Feb 3, 2005 (UTC)

42A75 Classical almost periodic functions, mean periodic functions

• PM: almost periodic function, id=6567 -- WP: almost periodic function -- Status: A

CryptoDerk 02:54, Feb 3, 2005 (UTC)

• PM: almost periodic function (equivalent definition), id=7214^new! -- WP: almost periodic function -- Status: A

Added to WP article some content motivated by this PM article. Ben Cairns 11:29, 18 April 2006 (UTC)

42A99 Miscellaneous

• PM: Poisson summation formula, id=4022 -- WP: Poisson summation formula -- Status: A

Entry is locked on PM. The author states "The reason that the entry is now inaccessible, when I adopted it from the orphanage, the proof contains serious errors, so I turned off access to it until I had a chance to replace it with a correct proof. This was done so that noone would be misled by an erroneous entry. I had left the project of repairing this proof on the back burner for a while, but now I will get back to it. As soon as I am done, I will make the entry accessible again and let you know." CryptoDerk 04:33, Feb 3, 2005 (UTC)

• PM: progressive function, id=5993 -- WP: progressive function -- Status: C

CryptoDerk 03:24, Feb 3, 2005 (UTC)

42B05 Fourier series and coefficients

• PM: Parseval equality, id=4717 -- WP: Parseval's theorem -- Status: A

CryptoDerk 03:44, Feb 3, 2005 (UTC)

• PM: Wirtinger's inequality, id=5393 -- WP: Wirtinger's inequality -- Status: C

CryptoDerk 03:59, Feb 3, 2005 (UTC)

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• PM: Balian-Low, id=7497^new! -- WP: Balian-Low theorem -- Status: C

Ben Cairns 12:03, 18 April 2006 (UTC)

42C99 Miscellaneous

• PM: an equivalent condition for the translates of an L_2 function to form a Riesz basis, id=7152^new! -- WP: Riesz sequence -- Status: C

Copied both Riesz sequence and Riesz basis to WP article. Ben Cairns 12:46, 18 April 2006 (UTC)